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IMSO 2019 — Math Division — Essay Question 5

IMSO Maths · IMSO 2019 — Math Division — Essay

Question 5

Consider the arrangements of $n$ identical circles, without overlapping, such that there are at least two rows of circles. Each circle should touch the next one in the same row and each circle except those on the bottom row should touch two circles on the row below it. For example, there are 7 possible arrangements for $n=6$ as shown in the diagram below.

Question illustration

Draw all the possible arrangements for $n=8$.